iEssentials of Stochastic ProcessesRick Durrett304050607010ͲSep10ͲJun10ͲMayat expiry01020500520540560580600620640660680700Almost Final Version of the 2nd Edition, December, 2011Copyright 2011, All rights reserved.

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iiPrefaceBetween the frst undergraduate course in probability and the frst graduatecourse that uses measure theory, there are a number oF courses that teachStochastic Processesto students with many di↵erent interests and with varyingdegrees oF mathematical sophistication. To allow readers (and instructors) tochoose their own level oF detail, many oF the prooFs begin with a nonrigorousanswer to the question “Why is this true?” Followed by aProofthat flls inthe missing details. As it is possible to drive a car without knowing about theworking oF the internal combustion engine, it is also possible to apply the theoryoF Markov chains without knowing the details oF the prooFs. It is my personalphilosophy that probability theory was developed to solve problems, so most oFour e↵ort will be spent on analyzing examples. Readers who want to master thesubject will have to do more than a Few oF the twenty dozen careFully chosenexercises.This book began as notes I typed in the spring oF 1997 as I was teachingORIE 361 at Cornell For the second time. In Spring 2009, the mathematicsdepartment there introduced its own version oF this course, MATH 474. Thisstarted me on the task oF preparing the second edition. The plan was to havethis fnished in Spring 2010 aFter the second time I taught the course, but whenMay rolled around completing the book lost out to getting ready to move toDurham aFter 25 years in Ithaca. In the ±all oF 2011, I taught Duke’s versionoF the course, Math 216, to 20 undergrads and 12 graduate students and overthe Christmas break the second edition was completed.The second edition di↵ers substantially From the frst, though curiously thelength and the number oF problems has remained roughly constant. Throughoutthe book there are many new examples and problems, with solutions that usethe TI-83 to eliminate the tedious details oF solving linear equations by hand.My students tell me I should just use MATLAB and maybe I will For the nextedition.The Markov chains chapter has been reorganized. The chapter on Poissonprocesses has moved up From third to second, and is now Followed by a treatmentoF the closely related topic oF renewal theory. Continuous time Markov chainsremain Fourth, with a new section on exit distributions and hitting times, andreduced coverage oF queueing networks. Martingales, a difcult subject Forstudents at this level, now comes fFth, in order to set the stage For their use ina new sixth chapter on mathematical fnance. The treatment oF fnance expandsthe two sections oF the previous treatment to include American options and thethe capital asset pricing model. Brownian motion makes a cameo appearancein the discussion oF the Black-Scholes theorem, but in contrast to the previousedition, is not discussed in detail.

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